Good, but please use the simplest notations so \begin{gather}u= f(x)+f_1(x)y+g(y)+g_1(y)x,\\u=f(x,y)+g(x,z)+h(y,z),\\u=\sin(x)\sin(y)+ f(x)+f_1(x)y+g(y)+g_1(y)x,\\u=-\cos(x)\cos(y)\cos(z)+f(x,y)+g(x,z)+h(y,z),\\u=-yz\cos(x)-xz\cos(y)-xy\cos(z)+f(x,y)+g(x,z)+h(y,z)\end{gather}